基于振动频率的响应面模型修正稳健估计法

A Robust Estimation Method for Response Surface Model Updating Based on Vibration Frequency

合理的结构有限元模型是进行结构评估的重要基础。为解决基于响应面法的有限元模型修正存在的多项式阶次选取规则不明和修正结果容易受优化目标质量影响的问题,以某斜拉桥为例,采用基于响应面的有限元模型修正方法,分析了多项式阶次与响应面精度、计算量之间的关系。将稳健估计法引入响应面优化求解过程,提高了基于响应面的模型修正的可靠性。分析了二阶多项式、三阶多项式和四阶多项式3种响应面模型,对比了3种响应面模型的响应面精度和计算量,对比了在优化目标与有限元指标差波动较大和较小2种工况下传统求解方法和稳健估计法的优化结果。结果表明:提高响应面模型的多项式阶次并不一定能提高响应面模型的精度,但随着多项式阶次的增加,响应面模型需要求解的未知参量急剧增加,增加了计算成本;在目标频率指标差波动较小的情况下,稳健估计求解法得到与传统最小二乘法相同的计算结果,当目标频率波动较大时,相较于最小二乘法,稳健估计法不会将指标差波动较大阶次的修正结果的误差传递到其他阶,最大条件地保证了修正结果的稳定性。

Reasonable FE model of structure is an important basis for structural evaluation.In order to solve the problem that the polynomial order selection rules of FE model correction based on the response surface method are not clear and the updating result is easy to be affected by the quality of optimization objective,taking a cable-stayed bridge for example,the relationship of polynomial order with accuracy of response surface and calculation amount is analyzed by using the response surface based FE model updating method.The robust estimation method is introduced into the response surface optimization solution process to improve the response surface based reliability of model updating.The response surface models of second-order polynomial,third-order polynomial and fourth-order polynomial are analyzed.The response surface accuracies and calculation amounts of the 3 response surface models are compared.The optimization results obtained by the traditional solution method and the robust estimation method under the conditions of larger and smaller fluctuations between the optimization objective and the FE indicator are compared.The result shows that(1) Increasing the polynomial order of the response surface model does not necessarily improve the accuracy of the response surface model,but as the polynomial order increased,the unknown parameters that need to be solved for the response surface model increased sharply,which increased the computational cost.(2) The robust estimation method obtained the same result as the traditional least squares method when the objective frequency indicator difference fluctuates smaller.While when the objective frequency indicator difference fluctuates larger,compared with the least squares method,the robust estimation method does not transfer the error of the updating result of the order with larger fluctuation in the indicator difference to other orders,which ensures the stability of the updating result to the greatest extent.